The discussion revolves around converting radians to degrees, minutes, and seconds, specifically focusing on two examples: 0.47623 radians and 0.25412 radians. Participants explore methods for performing these conversions, including step-by-step calculations and potential alternative approaches.
Participants generally agree on the method presented for the conversion, but there is uncertainty about whether simpler methods exist, leading to a discussion of alternative approaches.
The discussion does not resolve whether the proposed methods are the most efficient or if other methods might yield quicker results. There is also no consensus on the best approach to take for the second example (0.25412 radians).
MarkFL said:Okay, here is how I would work a):
First, let's get a decimal approximation for the number of degrees, with a good amount of precision:
$$0.47623\cdot\frac{180^{\circ}}{\pi}=\frac{85.7214}{\pi}^{\circ}\approx27.285969077515198^{\circ}$$
Okay, now we think of this as:
$$0.47623\approx27^{\circ}+0.285969077515198^{\circ}\cdot\frac{60'}{1^{\circ}}\approx27^{\circ}+17.15814465091188'$$
Continuing:
$$0.47623\approx27^{\circ}+17' + 0.15814465091188'\cdot\frac{60''}{1'}\approx27^{\circ}+17'+9.4886790547128''$$
Using standard notation and rounding some, we may write:
$$0.47623\approx27^{\circ}17'9.49''$$
RTCNTC said:There's got to be an easier way to do this, right?
MarkFL said:There could be, but that's the most straightforward way I know to do such a conversion by hand (i.e. without using a calculator programmed to do such conversions).